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I am trying to show that $$7!\cdot 6!=10!$$ but for some reason I don't see it. We can note that $7!=7\cdot 6!$ but what? Is there a general formula for the product of the factorials of two consecutive natural numbers?

5201314
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kormoran
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    can you show $2.3.4.5.6 = 8.9.10$ ? I mean if these were greater numbers maybe it would worth searching for a clever method, but not here. – zwim Apr 24 '21 at 14:39
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    https://math.stackexchange.com/questions/3903361/6-cdot-7-10-is-there-a-natural-bijection-between-s-6-times-s-7-and-s-1 aand ,https://math.stackexchange.com/questions/3958624/is-the-fact-that-67-10-a-pure-numerical-coincidence?noredirect=1 – Albus Dumbledore Apr 24 '21 at 14:40

1 Answers1

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$$6!=720=10×9×8.$$

So

$$10!=10×9×8×7!=720×7!=6!7!.$$

Is there any more to it than that.

Mike
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